**Acknowledgement**

This research was supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant numbers VR0063 & 488 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government. The author appreciates the editors for their comments and helps to improve this paper.

#### **4. References**

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equation computational strategies.

**3. Conclusions**

**Author details** 

**Acknowledgement** 

*The University of Ballarat, Australia* 

comments and helps to improve this paper.

Jiapu Zhang

studies of rotational inertia and its eigenvectors are called the principle axes of inertia.

where ||*di*||2 = (*a(i)x* 2 + *a(i)y* 2 + *a(i)z* 2) (*wx* 2 + *wy* 2 + *wz* 2) – ( *a(i)x wx* + *a(i)y wy* + *a(i)z wz* )2 . Thus, Eq. 17 can be easily solved by the canonical dual global optimization theory (Gao et al., 2012; Gao and Wu, 2012; Gao, 2000), by the ways of solving the canonical dual of Eq. 17 or solving the quadratic differential equations of the prime-dual Gao-Strang complementary function (Gao et al., 2012; Gao and Wu, 2012; Gao, 2000) through some ordinary or partial differential

To date the hydrophobic region AGAAAAGA palindrome (113-120) of the unstructured Nterminal region (1-123) of prions has little existing experimental structural data available. This Chapter successfully constructs three molecular structure models for AGAAAAGA palindrome (113-120) by using some suitable template 3NHD.pdb from Protein Data Bank and refinement of the Models with several optimization techniques within AMBER 11. These models should be very helpful for the experimental studies of the hydrophobic region AGAAAAGA palindrome of prion proteins (113-120) when the NMR or X-ray molecular structure of prion AGAAAAGA peptide has not been easily determined yet. These constructed Models for amyloid fibrils may be useful for the goals of medicinal chemistry.

This Chapter also introduces numerous practical computational approaches to construct the molecular models when it is difficult to obtain atomic-resolution structures of proteins with traditional experimental methods of X-ray and NMR etc, due to the unstable, noncrystalline and insoluble nature of these proteins. Known structures can be perfectly reproduced by these computational methods, which can be compared with contemporary methods. As we all know, X-ray crystallography finds the X-ray final structure of a protein, which usually need refinements using a SA protocol in order to produce a better structure. SA is a global search procedure and usually it is better to hybrid with local search procedures. Thus, the computational methods

introduced in this Chapter should be better than SA along to refine X-ray final structures.

This research was supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant numbers VR0063 & 488 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government. The author appreciates the editors for their

min (∑i=1 N ||*di*||2)2 subject to *w*T*w*=1, (17)

Furthermore, we may also notice that Eq. 13 can be rewritten as


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